The proof of a result analogous to that in Koelman and de Muynck [Phys. Lett. A 98, 1 (1983)] is given for the case of unbounded observables. If two, not necessarily bounded, observables are represented by a positive operator-valued measure, then the measurement of any of them is undisturbed if and only if they commute. The Naimark theorem on dilations of spectral functions is exploited. A stronger version of Wigner’s theorem is given.
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Kruszyński et al. (1987) studied this question.
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